In 2016, a very coordinated and limber Ya Boi Kev (Kevin), who enjoy running around on all fours, graciously offered a quick tutorial for anyone interested in doing the same. He first cautioned to start off very slowly so as not to immediately face plant and suggested that practice makes perfect.
In my style four legged running, I usually have the right arm come forward as the left leg comes forward and then I would have the left leg come forward as the right arm comes forward. Ultimately it just takes a lot of practice.
A couple of years later, Kevin explained why he loves quadruped running.
Here’s an example of Kevin running on all fours.